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A note on commutators in free products. II

Published online by Cambridge University Press:  24 October 2008

H. B. Griffiths
H. B. Griffiths
Affiliation:
Department of MathematicsUniversity of Bristol
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Extract

The purpose of this note is to improve Theorem 1·1 of (1) to the following result:

Theorem 1. Let H be the ordinary free product of a sequence of groups Gn, and let m be any integer > 0. If

where each gi є Gi and is not the identity, then h is not equal to any product of fewer than m commutators from H.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 51 , Issue 2 , April 1955 , pp. 245 - 251
Copyright
Copyright © Cambridge Philosophical Society 1955

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References

REFERENCES

(1)Griffiths, H. B.A note on commutators in free products. Proc. Camb. phil. Soc. 50 (1954), 178–88.CrossRefGoogle Scholar
(2)Van Der Waerden, B. L.Free products of groups. Amer. J. Math. 70 (1948), 527–8.CrossRefGoogle Scholar